Three-dimensional board game apparatus

ABSTRACT

A game of skill including a three-dimensional playing board and opposing playing pieces adapted to be moved according to predetermined rules on said playing board to achieve a winning objective. The board is generally diamond shaped and includes three groups of square playing spaces, the playing spaces of each group having surfaces located in parallel planes perpendicular to the planes of the playing spaces of the other two groups. Each playing space is joined to at least a playing space of each of the other groups at two of its edges to form a multiplicity of cube corners. The game pieces and game board cooperate to hold the game pieces in playing spaces regardless of the orientation thereof.

' [451 Feb. 12, 1974 United States Patent 1191 Gold [ THREE-DIMENSIONALBOARD GAME Primary Examiner-Delbert B. Lowe Attorney, Agent, orFirmAlfred E. Corrigan; Robert APPARATUS I [76] inventor: Nicholas Gold,72 Morningside Dr., Corb Arlington, Mass. 02174 Mar. 8, 1972 Appl. No.:232,849

ABSTRACT [22] Filed:

game of skill including a three-dimensional playing board and opposingplaying pieces adapted to be moved according to predetermined rules onsaid play- [52] US. Cl. 273/131 AD, 273/131 BA, 273/136 B,

ing board to achieve a winning objective. The board is f'each lel planesperof the d to at least a playing space of each of the other groups attwo of its ed generally diamond shaped and includes three groups ofsquare playing spaces, the playing spaces 0 group having surfaceslocated in paral pendicular to the planes of the playing spaces othertwo groups. Each playing space is joine [56] References Cited UNITEDSTATES PATENTS ges to form a multiplicity of cube corners.

mm 6 mm C 0w 74 2 2577 9999 1111 47 9 790 0002] 3237- 7-o07.9 231.

The game pieces and game board cooperate to hold the game pieces inplaying spaces regardless of the orientation thereof.

N R KW 11 0] ay N 7 2 Mayer Martin 23 Claims, 4 Drawing Figures i f 2 ITHREE-DIMENSIONAL BOARD GAME APPARATUS BACKGROUND OF THE INVENTION Thepresent invention is concerned with a game of skill such as checkers orchess, in which opposing game pieces are moved according topredetermined rules with respect to playing spaces on a game board. Thecomplexity, skill, challenge and variations in strategy of such gamesdepend upon the number of game pieces and the rules governing theirmovements relative to the board on which the game is played as well asthe relationship of each piece to every other piece. The complexity,challenge and strategy considerations of such games are considerablyincreased by adding a third dimensional relationship or consideration toa game involving sets of game pieces each movable into two dimensions,e.g., three-dimensional tic-tac-toe, checkers,

chess, etc. in which the game board or structure on which the gamepieces are played comprises a plurality of two-dimensional areas havingplaying spaces and in each of which each player controls the movement ofa separate set of game pieces.

SUMMARY OF THE INVENTION Objects of the present invention are: toprovide a game of the type described in which each player has a singleset of game pieces and each game piece is movable in three dimensions;to provide a threedimensional game board that is simple, easy andinexpensive to construct, yet, in combination with a very few gamepieces, provides a game of skill having numerous variations and degreesof complexity of strategy limited only by the imagination andinnovativeness of the players in devising the rules of play; and toprovide a three-dimensional game in which the playing board or structurecan be formed of sheet material; in which the number of playing spacescan be varied; in which the number of playing pieces per player is asfew as two or three depending upon the rules and number of players; andwhich can be played by two, three or four players simultaneouslydepending upon the number of sets of game pieces and the rules governingplay.

These and other objects of the invention are realized in a gameutilizing a novel game board similar to a chess board in that it iscomposed of square, contiguous playing spaces, but differing in a noveland unobvious way which adds to the complexity and interest of the game,by virtue of the fact that each playing space is adjoined by twomutually perpendicular playing spaces cooperating therewith to form acube corner. Thus the playing board" or surface is composed of amultiplicity of cube corners combined to form a generally diamond-shapedstructure adapted to be formed of sheet material and supported on ahorizontal surface with the playing spaces nominally disposed in threemutually perpendicular planes each at an angle relative to thehorizontal playing surface. The game base formed, for example, of aferromagnetic material (sheet steel) is designed to cooperate with thegame pieces, which in the same example include magnets for retaining thegame pieces in the playing spaces regardless of the orientation of thesurfaces of the playing spaces.

Other objects of the invention will in part be obvious and will in partappear hereinafter.

The invention accordingly comprises the apparatus possessing theconstruction, combination of elements and arangement of parts which areexemplified in the following detailed disclosure, and the scope of theapplication of which will be indicated in the claims.

For a fuller understanding of the nature and objects of the invention,reference should be had to the following detailed description taken inconnection with the accompanying drawing wherein:

FIG. 1 is a perspective view illustrating the form and development ofthe game board of the invention;

FIG. 2 is a plan view of a game board embodying the invention;

FIG. 3 is a sectional view taken substantially along the line 3-3 ofFIG. 2; and

FIG. 4 is a plan view, similar to FIG. 2, showing another embodiment ofthe game board of the invention.

Reference is now made to FIG. 1 of the drawing wherein there is shown anassembly of threedimensional parallelepipedons illustrating theconfiguration of the three-dimensional playing surface of the game boardof the invention. While the structure shown in FIG. 1 can be employed asa component of and in playing the game of the invention, it is shown forthe primary purpose of facilitating understanding of the development andshape of the three-dimensional playing surface rather than the preferredstructure which is illustrated in FIGS. 2 and 3. The playing surfaceillustrated in FIG. 1 is composed of a multiplicity of square surfacestermed playing spaces divided into three groups with the surfaces of theplaying spaces of each group located in a plurality of sub-groupsdisposed in parallel planes perpendicular to the planes of the surfacesof the other two groups. Nominally, theplanes may be horizontal andvertical with each square playing space of any group being joined at atleast two edges by playing spaces of the other two groups to form amultiplicity of cube corners, i.e., three sides of a cube. For thepurpose of description and to facilitate understanding, the surfaces ofone group are shown as horizontal and the surfaces of the other twogroups vertical, one facing left and the other right.

As will be seen from FIG. 1, the playing surface is generally diamondshaped having a horizontal playing space at each corner with the maximumnumber of horizontal playing spaces in the two longest (cornertocorner)rows being equal. Thus, the playing board shown for purposes ofillustration may be described as a 4 X 4 board containing 16 4 X 4playing spaces of one group and l2 (3 X 4) playing spaces of each of theother two groups. Although the 4 X 4 board is preferred for one versionof the game contemplated to be played on the board, a 3 X 3 board couldbe employed and would contain about the minimum number of playingspaces, i.e., 21, that would provide an interesting and challenging gamefor two players. Of course, th board size, in terms of playing spaces,can be increased substantially and this may prove necessary when morethan two persons are to play. The minimum size will depend upon thenumber of playing pieces and the rules governing their movement as willappear hereinafter.

For the purposes of description, the horizontalappearing playing spacesare designated 10, the leftfacing vertical appearing playing spaces aredesignated 20 and the right-facing spaces are designated 30. In FIG. 2,the playing spaces corresponding to spaces 10 are shown as being white,spaces 20 as grey and spaces 30 as black. The number of playing spacesis equal to n where n is an integer, e.g., 4, as shown, while there aren(n-l) of each of playing spaces and 30 so that the total number ofplaying spaces is equal to 3n 2n.

The game surface illustrated in FIG. 1 can be formed in a number ofways, for example, of a multiplicity of parallelepipedons each having asquare cross section and a length which is a multiple of a side of thesquare. Thus horizontal playing space designated 10a is the uppersurface of a cube while spaces 10b are upper surfaces ofparallelepipedons two squares high and spaces 20b and 30b are each asquare portion of a side of the last mentioned parallelepipedons.Similarly, for example, playing spaces 10c, 20c and 30c are the uppersurface and square portions of two side vertical surfaces, respectively,of a parallelepipedon seven squares (or cubes) high.

The preferred form of playing board is adapted, for the sake ofconvenience, to be supported on a horizontal surface such as a table andis illustrated in FIGS. 2 and 3. The playing board, designated 40, isdesigned to be fabricated of sheet material by conventional processessuch as pressed sheet metal or an artificial plastic formed, forexample, by conventional vacuum forming or molding techniques. Theactual playing surface of board 40 is substantially the same as thatshown in FIG. 1 and comprises three sets of square playing areas shownas white, grey and black, with planar surfaces lying in parallel planes,each adjoined at two edges by mutually perpendicular playing surfaces oftwo other sets. As previously noted, the playing spaces combine to forma game surface comprising a multiplicity of internal and external,contiguous cube corners. Board 40 is generally diamond shaped with theplaying surfaces or areas surrounded by a skirt 42 terminating in anedge 44 lying in a plane and adapted to support the individual playingspace surfaces disposed at an angle with respect to the plane of edge44.

Another embodiment of the game board of the invention is illustrated inFIG. 4 which shows one half of the board, the playing surface of whichis substantially the same as that shown in FIG. 2. The board is dividedalong a line or plane intersecting the playing surface at the corners ofcube faces 82, 83, 85 and 84 so that the two halves of the playingsurface can be pivoted about the dividing line into superposed,face-to-face relation. The board is rectangular and includes aperipheral section generally designated 90 having a dependent skirt (notshown) with a lower edge or surface similar to edge 44 locatedsubstantially in a plane for supporting the board on a plane surface.The peripheral section includes four corner portions designated 92formed with triangular recesses 94 for holding game pieces.

The two halves of the board are preferably pivotally connected to oneanother by conventional hinge means, e.g., a flexible strip of material96, permitting the halves to be pivoted into a closed or folded positionin which the playing surfaces as well as the upper surfaces of theperipheral sections of the two halves are disposed in face-to-face,contiguous relation. In this closed or folded position, the board is notonly substantially smaller and compact, but the recesses 94 cooperate toform. containers or compartments for holding and carrying the playingpieces. Suitable latch means (not shown) of a conventional type may beprovided for retaining the two halves in the folded position.

In the form shown, the game includes and is adapted to be played with atleast two sets of playing pieces by two opposing players. Each setincludes three playing pieces, the pieces of one set being shown ascircular discs designated 50, 52 and 54 and the pieces of the other setbeing shown as square discs designated-60, 62 and 64. Of course, theplaying pieces of each set may be distinguished from one another andfrom the pieces of another set by any number of conventional means inaddition to shape, such as size, color, and/or indicia, etc; or by othermeans which will be described hereinafter. Distinguishing the individualpieces of a set enables the players to prescribe rules for the movementof each piece as well as its relationship to all other pieces.

The board and playing pieces include mutually cooperative means of aconventional type for retaining the playing pieces in place withinplaying spaces. For example, the board may be formed of a ferromagneticmaterial (i.e. steel) and each playing piece may incorporate a magnet.In the case of a plastic or nonferrous board, each playing space may beformed with a hole or recess for receiving a projection on the undersideof each playing piece. Other well known attachment or fastening meansmay also be employed and are considered to fall within the scope of theinvention.

In a typical two player game illustrated, each player has three playingpieces initially arranged as shown, with pieces 50 and 60, eachdesignated with the letter S, disposed in playing spaces 56 and 66,respectively, located at opposite ends of the board. The object of thegame is to move pieces 50 and 60 to the space (56 or 66) initiallyoccupied by the opponents piece at the opposite end of the board, theplayer first to arrive being the winner. It will be noted that pieces 52and 54 are located in spaces 58 and 59 adjoining space 56 on two sidesand pieces 62 and 64 are similarly located in spaces 68 and 69 adjoiningspace 66.

The rules for movement of the playing pieces and their relationship toone another may be similar to checkers or chess. For example, pieces 50and 60 can be moved in any direction, one space at a time, and can take"or capture an opponents piece by moving into the playing space occupiedby the latter, but should not be moved into or remain in a playing spacewhere it may be taken or captured. According to a typical set of rules,pieces 52 and 62 may be moved in any direction, one space at a time,around an edge or corner to any adjoining space; and pieces 54 and 64can be moved in the same manner as pieces 52 and 62, or as far asdesired in any single plane. For example, piece 54 can be shifted ormoved in a plane from space 59 to any of spaces 70, 72 or 74 in a singlemove. Similarly, piece 64 can be moved in the same manner, for example,from space 69 to any of spaces 76, 78 or 80 in a single move. Pieces 54and 64 can also be shifted in one direction as far as desired in theplanes which run from left to right (as viewed in FIG. 2), e.g., ifpiece 54 or 64 were located in space 82, it could be moved to either ofspaces 83, and 84. The number of spaces that pieces 54 or 64 can bemoved at one time in the abovedescribed planes is limited when anopponents piece occupies one of the spaces in the plane in which piece54 or 64 is located. For example, if an opponents piece were located inplaying space 72, piece 54, as shown in FIG. 2, could only move twospaces in the plane containing playing spaces 59, 70, 72 and 74 and thenwould have to stop in playing space 72 to capture the opponents piece.

It will be apparent that the rules governing the movement of each piece,such as whether it can be advanced in only one direction, e.g., towardthe goal, or moved in any direction or plane, the number of spaces itcan be advanced during each move, etc.; and the relationship betweenpieces, such as'whether they can take 0pponents pieces, block or jumpover other pieces, etc., are almost infinitely variable and can vastlyaffect the strategy and complexity of the game. Additional pieces may beadded to each set with particular rules governing their moves andrelationships. For example, a game similar to so-called Chinese Checkersmay be played in which the object is to move all of ones pieces into theplaying spaces originally occupied by the opponents pieces. Here again,the three-dimensional configuration of the playing surface heightens thecomplexity of the game as well as the skill required and the interestgenerated.

As previously noted, if the board includes asufficient number of playingspaces, e.g., 96 spaces for a 6 X 6 board, essentially the same game canbe played by three persons, the third set of pieces being arranged at athird corner in spaces 74, 80 and 82, for example, with the winningobjective being to be the first to move the piece initially occupyingeach of spaces 56, 66 and 82 into the fourth corner space 84. When afourth person is playing, his pieces are similarly arranged in spaces84, 86 and 88 and the object of the game may be for each player to befirst to move his corner piece (designated S) into another corner space.

It will be seen that, with the novel, yet relatively simple,three-dimensional playing board of the invention and a relatively fewplaying pieces, it is possible to create a complex and challenging gameinvolving an almost infinite variety and number of strategies and gameobjectives. The variations and complexities of the games which can beplayed are limited only by the imaginations of the players insofar asthey determine the rules of the play. Not only are the game variationsalmost literally boundless, but more than two persons can play at thesame time, further adding to the game complexity and interest andchallenge to the players.

Since certain changes may be made in the above apparatus withoutdeparting from the scope of the invention herein involved, it isintended that all matter contained in the above description or shown inthe accompanying drawing shall be interpreted as illustrative and not ina limiting sense.

What is claimed is:

1. A three-dimensional game comprising, in combination:

two sets of game pieces each including a plurality of piecesindividually distinguishable from one another and said pieces of saidother set;

a game board having a three-dimensional playing surface including threegroups of substantially square playing spaces, each group of saidplaying spaces comprising a plurality of sub-groups, each of saidsub-groups lying in one of a plurality of substantially parallel planes,each of said plurality of parallel planes of each group beingsubstantially perpendicular to each of the pluralities of parallelplanes of the other two groups, said playing spaces of each of saidsub-groups each having at least a marginal surface portion locatedsubstantially in a common plane so that each of said playing spacesincludes at least two linear edges joined to the linear edges ofadjacent playing spaces belonging to the other two groups to form saidplaying surface; and

means for retaining each of said game pieces within a playing spaceregardless of the orientation of said plane thereof.

2. A three-dimensional game as described in claim 1 wherein the surfacesof said playing spaces are generally planar and at least two of saidsurfaces of each of said groups are disposed in spaced substantiallyparallel planes.

3. A three-dimensional game as described in claim 2 wherein said surfaceof each of said playing spaces of one of said groups joins said surfacesof said playing spaces of said other groups at at least two edges toform a plurality of cube comers.

4. A three-dimensional game as described in claim 3 wherein said gameboard is formed of a sheet material.

5. A three-dimensional game as described in claim 1 wherein said gameboard includes means adapted to support said game board on asubstantially horizontal surface with all of said surfaces of saidplaying spaces disposed at an acute angle with respect to saidhorizontal supporting surface.

6. A three-dimensional game comprising, in combination:

two sets of game pieces each including a plurality of piecesindividually distinguishable from one another and said pieces of saidother set;

a game board having a three-dimensional playing surface including threegroups of substantially square playing spaces each having at least amarginal surface portion located substantially in a plane, said planesof each of said groups of spaces being substantially perpendicular tosaid planes of the other two groups so that each of said playing spacesincludes at least two linear edges joined to the linear edges ofadjacent playing spaces belonging to the other two groups to form saidplaying surface, said playing surface being generally diamond shaped andincluding a playing space of one of said groups at each of the fourcorners thereof; and

means for retaining each of said game pieces within a playing spaceregardless of the orientation of said plane thereof.

7. A three-dimensional game as defined in claim 6 wherein said gameboard is divided into two sections along a plane through the corners ofsaid playing spaces of said one group including said spaces at oppositecorners of said playing surface.

8. A three-dimensional game as defined in claim 7 wherein said sectionsare connected for pivotal movement into a folded position in which thetwo sections of said playing surface are in superposed, face-to-facerelation.

9. A three-dimensional game as defined in claim 6 wherein said one groupis composed of n playing spaces and each of said other groups iscomposed of n(nl) playing spaces.

10. A three-dimensional game as defined in claim 9 wherein n equals atleast four.

11. A three-dimensional game as defined in claim 6 wherein said playingspaces have substantially planar surfaces and said surfaces of each ofsaid groups are disposed in substantially parallel planes perpendicularto said planes of said playing spaces of the other two groups.

12. A three-dimensional game as defined in claim 6 wherein said gameboard is formed of a sheet material.

13. A three-dimensional game board as defined in claim 6 wherein saidretaining means includes at least a portion of said game board formed ofa ferromagnetic material and each of said game pieces including amagnet.

14. A three-dimensional game as defined in claim 12 wherein each of saidplaying spaces has a substantially planar surface intersecting thesurfaces of adjoining playing spaces at substantially right anglesthereto.

15. A three-dimensional game as defined in claim 14 wherein said gameboard includes means for supporting said board on a substantiallyhorizontal surface with all of said surfaces of said playing spacesdisposed at an angle with respect to said horizontal supporting surface.

16. A three-dimensional game as defined in claim 15 wherein thelast-mentioned means include a border surrounding said playing surfaceand having a dependent skirt for supporting said board.

17. A three-dimensional game as defined in claim 16 wherein said borderis rectangular.

18. A three-dimensional game as defined in claim 17 wherein said borderincludes comer portions formed with recesses for holding said gamepieces.

19. A three-dimensional game as defined in claim l8 wherein said boardis divided into two sections along a plane through corners ofsaidplaying spaces of said one group including said spaces at oppositecomers of said playing surface, and said sections are pivotallyconnected to one another for movement into a folded position in whichthe two sections of said playing surface and the surface of said borderare in face-to-face relation and said recessed corner portions cooperateto form at least one container for said game pieces.

20. A three-dimensional game board adapted for use with a plurality ofgame pieces, said game board having a generally diamond shape andcomprising three groups of substantially square playing spaces, saidplaying spaces of each of said groups having surfaces arranged insubstantially parallel planes perpendicular to said planes of saidplaying spaces of the other two groups; each of said playing spacesbeing joined along at least two'edges to said playing spaces of saidother two groups to form a multiplicity of cube corners; and each ofsaid playing spaces including means adapted to cooperate with a gamepiece for retaining it within the playing space.

21. A three-dimensional game board as defined in claim 20 whereinplaying spaces of one of said groups are located near the extremities ofsaid board.

22. A three-dimensional game board as defined in claim 21 wherein saidone group is composed of n playing spaces and the other two groups areeach composed of n(n-1) playing spaces.

23. A three-dimensional game board as defined in claim 22 wherein nequals at least four.

1. A three-dimensional game comprising, in combination: two sets of gamepieces each including a plurality of pieces individually distinguishablefrom one another and said pieces of said other set; a game board havinga three-dimensional playing surface including three groups ofsubstantially square playing spaces, each group of said playing spacescomprising a plurality of sub-groups, each of said sub-groups lying inone of a plurality of substantially parallel planes, each of saidplurality of parallel planes of each group being substantiallyperpendicular to each of the pluralities of parallel planes of the othertwo groups, said playing spaces of each of said sub-groups each havingat least a marginal surface portion located substantially in a commonplane so that each of said playing spaces includes at least two linearedges joined to the linear edges of adjacent playing spaces belonging tothe other two groups to form said playing surface; and means forretaining each of said game pieces within a playing space regardless ofthe orientation of said plane thereof.
 2. A three-dimensional game asdescribed in claim 1 wherein the surfaces of said playing spaces aregenerally planar and at least two of said surfaces of each of saidgroups are disposed in spaced substantially parallel planes.
 3. Athree-dimensional game as described in claim 2 wherein said surface ofeach of said playing spaces of one of said groups joins said surfaces ofsaid playing spaces of said other groups at at least two edges to form aplurality of cube corners.
 4. A three-dimensional game as described inclaim 3 wherein said game board is formed of a sheet material.
 5. Athree-dimensional game as described in claim 1 wherein said game boardincludes means adapted to support said game board on a substantiallyhorizontal surface with all of said surfaces of said playing spacesdisposed at an acute angle with respect to said horizontal supportingsurface.
 6. A three-dimensional game comprising, in combination: twosets of game pieces each inCluding a plurality of pieces individuallydistinguishable from one another and said pieces of said other set; agame board having a three-dimensional playing surface including threegroups of substantially square playing spaces each having at least amarginal surface portion located substantially in a plane, said planesof each of said groups of spaces being substantially perpendicular tosaid planes of the other two groups so that each of said playing spacesincludes at least two linear edges joined to the linear edges ofadjacent playing spaces belonging to the other two groups to form saidplaying surface, said playing surface being generally diamond shaped andincluding a playing space of one of said groups at each of the fourcorners thereof; and means for retaining each of said game pieces withina playing space regardless of the orientation of said plane thereof. 7.A three-dimensional game as defined in claim 6 wherein said game boardis divided into two sections along a plane through the corners of saidplaying spaces of said one group including said spaces at oppositecorners of said playing surface.
 8. A three-dimensional game as definedin claim 7 wherein said sections are connected for pivotal movement intoa folded position in which the two sections of said playing surface arein superposed, face-to-face relation.
 9. A three-dimensional game asdefined in claim 6 wherein said one group is composed of n2 playingspaces and each of said other groups is composed of n(n-1) playingspaces.
 10. A three-dimensional game as defined in claim 9 wherein nequals at least four.
 11. A three-dimensional game as defined in claim 6wherein said playing spaces have substantially planar surfaces and saidsurfaces of each of said groups are disposed in substantially parallelplanes perpendicular to said planes of said playing spaces of the othertwo groups.
 12. A three-dimensional game as defined in claim 6 whereinsaid game board is formed of a sheet material.
 13. A three-dimensionalgame board as defined in claim 6 wherein said retaining means includesat least a portion of said game board formed of a ferromagnetic materialand each of said game pieces including a magnet.
 14. A three-dimensionalgame as defined in claim 12 wherein each of said playing spaces has asubstantially planar surface intersecting the surfaces of adjoiningplaying spaces at substantially right angles thereto.
 15. Athree-dimensional game as defined in claim 14 wherein said game boardincludes means for supporting said board on a substantially horizontalsurface with all of said surfaces of said playing spaces disposed at anangle with respect to said horizontal supporting surface.
 16. Athree-dimensional game as defined in claim 15 wherein the last-mentionedmeans include a border surrounding said playing surface and having adependent skirt for supporting said board.
 17. A three-dimensional gameas defined in claim 16 wherein said border is rectangular.
 18. Athree-dimensional game as defined in claim 17 wherein said borderincludes corner portions formed with recesses for holding said gamepieces.
 19. A three-dimensional game as defined in claim 18 wherein saidboard is divided into two sections along a plane through corners of saidplaying spaces of said one group including said spaces at oppositecorners of said playing surface, and said sections are pivotallyconnected to one another for movement into a folded position in whichthe two sections of said playing surface and the surface of said borderare in face-to-face relation and said recessed corner portions cooperateto form at least one container for said game pieces.
 20. Athree-dimensional game board adapted for use with a plurality of gamepieces, said game board having a generally diamond shape and comprisingthree groups of substantially square playing spaces, said playing spacesof each of said groups having surfaces arranged in substantiallyparallel planes Perpendicular to said planes of said playing spaces ofthe other two groups; each of said playing spaces being joined along atleast two edges to said playing spaces of said other two groups to forma multiplicity of cube corners; and each of said playing spacesincluding means adapted to cooperate with a game piece for retaining itwithin the playing space.
 21. A three-dimensional game board as definedin claim 20 wherein playing spaces of one of said groups are locatednear the extremities of said board.
 22. A three-dimensional game boardas defined in claim 21 wherein said one group is composed of n2 playingspaces and the other two groups are each composed of n(n-1) playingspaces.
 23. A three-dimensional game board as defined in claim 22wherein n equals at least four.